Answer:
-8
Step-by-step explanation:
For roots r and s, the quadratic can be factored ...
f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs
Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...
r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2
Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...
(x-coefficient)^2 -2(constant term)
we get ...
r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6
r^2 +s^2 = 2(m -1)^2 -8
The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.
help
Use the dot product to find [v] when v =(-2,-1)
A.-1
b.-3
c;sqr5
dsqr3
Answer:
sqrt(5)
Step-by-step explanation:
Honestly think this person means to find the magnitude of the vector. You can use dot product here, the vector with itself... But that isn't the last step.
v dot v=4+1=5
and so |v|=sqrt(5)
In a glide reflection, what comes first and what comes second?
Answer:
A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. ... The first one is a translation rule.
Final answer:
In a glide reflection, the translation occurs first, moving the figure along a straight line, followed by a reflection over a line parallel to the translation vector, resulting in a figure that has been moved and potentially reoriented.
Explanation:
In a glide reflection, a transformation that combines a translation with a reflection, the proper sequence is important. The translation part comes first, where the figure is slid along a straight line called the translation vector. After the figure has been moved, the second step is the reflection over a line parallel to the vector of the translation. This two-step process results in a final image that has the same size and shape as the original figure but is in a different position and may have a different orientation.
Imagine a point undergoing a glide reflection. Initially, it is translated along a vector, and then it is reflected across a line that is parallel to the direction of translation. The end result is that the point has 'glided' to a new location, as if it had slid across a mirror placed at an angle to its original path.
(6m5 + 3 – m3 – 4m) – (–m5 + 2m3 – 4m + 6)
Answer: [tex]7m^5-3m^3-3[/tex]
Step-by-step explanation:
You can observe that you need to subtract the polynomial [tex](6m^5 + 3 - m^3 -4m)[/tex] and the polynomial [tex](-m^5 + 2m^3- 4m + 6)[/tex].
It is important the remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]
Then, the first step is to distribute the negative sign:
[tex](6m^5 + 3 - m^3 -4m)-(-m^5 + 2m^3- 4m + 6)=\\=6m^5 + 3 - m^3 -4m+m^5-2m^3+ 4m- 6[/tex]
And finally you must add the like terms. Then:
[tex]=7m^5-3m^3-3[/tex]
URGENT WILL GIVE BRAINLIEST
Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.
Answer:
(5sqrt(2), 45 deg)
(-5sqrt(2), 225 deg)
Step-by-step explanation:
(x,y)=(5,5)
So theta=arctan(5/5)=arctan(1)=45 degrees
Now r! r=sqrt(x^2+y^2)=sqrt(5^2+5^2)=sqrt(50)=sqrt(25)sqrt(2)=5sqrt(2)
So one polar point is (5sqrt(2) , 45 degrees)
Now if we do 180+45=225 degrees... this puts us in the 3rd quadrant... to get back to quadrant 1 we just take the opposite of our r
so another point is (-5sqrt(2) , 225 degrees)
value of (–3/8) × (+8/15).
A. 11/15
B. 11/23
C. –1/5
D. –1/3
ANSWER
The correct answer is C
EXPLANATION
We want to find the value of
[tex] - \frac{3}{8} \times \frac{8}{15} [/tex]
This is the same as:
[tex] - \frac{3}{8} \times \frac{8}{3 \times 5} [/tex]
We cancel out the common factors to get:
[tex]- \frac{1}{1} \times \frac{1}{1 \times 5} [/tex]
We simplify to get:
[tex] - \frac{1}{5} [/tex]
The correct answer is C
Solve the equation. 42x – 5 = 64
Answer:
x =23/14
If we want to change it to a mixed number
x = 1 9/14
Step-by-step explanation:
42x – 5 = 64
Add 5 to each side
42x – 5+5 = 64+5
42x = 69
Divide each side by 42
42x/42 = 69/42
x = 69/42
Divide the top and bottom by 3
x =23/14
If we want to change it to a mixed number
x = 1 9/14
Answer:
d)4
Step-by-step explanation:
Need help with math question
Answer:
720
Step-by-step explanation:
Answer:
720
Step-by-step explanation:
We are given the following permutation problem to solve:
[tex] _ 6 P _ 6 [/tex]
We know that the number of possibilities to choose an ordered set of [tex] r [/tex] objects from a total of [tex]n[/tex] objects is given by:
[tex] _ n P _ r = \frac { n ! } { ( n - r ) ! } [/tex]
Substituting the given values, n = 6, r = 6:
[tex] _ 6 P _ 6 = \frac { 6 ! } { ( 6 - 6 ) ! } [/tex] = 720
The ideal temperature of a freezer to store a particular brand of ice cream is 0°F, with a fluctuation of no more than 2°F. Which inequality represents this situation if t is the temperature of the freezer?
Answer:
| x - 0 | ≤ 2
Step-by-step explanation:
Given,
The ideal temperature of the freezer = 0° F,
Also, it can fluctuate by 2° F,
Thus, if x represents the temperature of the freezer,
Then, there can be two cases,
Case 1 : x > 0,
⇒ x - 0 ≤ 2
Case 2 : If x < 0,
⇒ 0 - x ≤ 2,
⇒ -( x - 0 ) ≤ 2,
By combining the inequalities,
We get,
| x - 0 | ≤ 2,
Which is the required inequality.
The midpoint of UV is point W. What are the coordinates of point V?
(–6, –14)
(2, –23)
its B.
Answer:
B). (2, –23)
Well this person made it easy by literally saying the answer...
Step-by-step explanation:
Hope this helps!! Also heart and rate if you found this answer helpful!!
The correct option is, (B) (2, –23).
What is called co-ordinate?Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions (2D) or in space of three dimensions ( 3D ). There are several coordinate schemes commonly used by mathematicians, scientists, and engineers.What is co-ordinate with example?A set of values that show an exact position. On graphs it is usually a pair of numbers: the first number shows the distance along, and the second number shows the distance up or down.Example: the point (12,5) is 12 units along, and 5 units up.What is the co ordinate formula?One of the important formula of coordinate geometry is the equation of the straight line which is y = mx + c. Here m is the slope and c is the y-intercept (tan θ = m, here θ is the angle that the line makes with the positive x-axis).What is coordinate of a point?The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.Learn more about coordinates here:
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At which x-values are the output values of the floor function g(x) = ?x? and the ceiling function h(x) = ?x? equal? Check all that apply. –8 –5.2 –1.7 0 2.4
Answer:
-8, 0
Step-by-step explanation:
The floor and ceiling functions have equal values for any integer argument. Their value is that integer.
Among your answer choices, the integers are -8 and 0.
Answer:
-8 and 0 or A and D
Step-by-step explanation:
Just took it on Edge 2020
Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below.
(0, 0) and 2/3
Answer:
see below
Step-by-step explanation:
A proportional relationship has a graph that always goes through the origin. This fact by itself eliminates all the wrong answers.
A slope of 2/3 means the rise is 2 for each horizontal run to the right of 3. The two given points are 2 vertical units and 3 horizontal units apart, demonstrating a slope of 2/3.
Sameena measures the angle from the ground to the top of a building from two locations. The angle of elevation from the first point is 45°, and the angle of elevation from the second point is 60°. The distance from the second point to the top of the building is 150 ft.
[Not drawn to scale]
What is the distance from the first observation point to the top of the tower (x)? Round the answer to the nearest tenth.
122.5 ft
183.7 ft
244.9 ft
501.9 ft
Answer:
183.7 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation between the hypotenuse and opposite side in a right triangle is ...
Sin = Opposite/Hypotenuse
For the first observation, the angle is 45° and the length of the hypotenuse of the triangle is given as x. For the second observation, the opposite side (building height) is the same, the angle is 60°, and the hypotenuse is 150 ft.
We can multiply the above equation by "Hypotenuse" to get an expression for "Opposite".
Opposite = Sin×Hypotenuse
For our two observations, this becomes ...
sin(45°)·x = (building height) = sin(60°)·(150 ft)
Dividing by the coefficient of x, we have ...
x = (150 ft)·sin(60°)/sin(45°) ≈ 183.7 ft
Answer:
B: 183.7
Step-by-step explanation:
First we need to find our values
A = 45°
B = 180 - 60 = 120
a = 150
Then we can solve for x using this formula x = a * sin(B)/sin(A).
x = 150 * sin(120)/sin(45)
x = 150 * √6/2
x = 75√6
x = 183.71173
Johnny deposited $1230 in a savings account at 2.25 percent interest. How much interest will the account earn in 10 years?
$212.50
$291.25
$276.75
$202.25
Will got an insurance check of $4500 after a car accident. He deposited it into a savings
account at 1.7 percent interest for five years. What was the total amount of money in the
account after five years?
1. $4462.50 2. $4882.50 3. $4374.38 4. $4315.63
Answer:
276.75
Step-by-step explanation:
Deposit 1230. paying 2.25 % 10 yrs.
the interest is 276.75 and the amount is 1506.75
Answer:
The answer to the first question is $276.75 and the answer to the second question is $4882.50
Step-by-step explanation:
Johnny deposited $1230 in a savings account at 2.25 percent interest. How much interest will the account earn in 10 years?
To solve this, we simply use the simple interest formula;
Simple Interest = PRT / 100
where p is the principal, R is the rate and T is the time (in years)
In this question principal = $1230 rate = 2.25 and time = 10
We can now plug the variables into the formula;
Simple Interest = PRT / 100
=$1230 × 2.25× 10 / 100
= $27675 / 100
= $276.75
Therefore, the amount of interest earn in 10 years is $276.75
Will got an insurance check of $4500 after a car accident. He deposited it into a savings account at 1.7 percent interest for five years. What was the total amount of money in the account after five years?
We can also solve this second part of the question using the simple interest formula, here;
principal = $4500
Rate =1.7
Time =5
We will now insert our values into the simple interest formula, thus;
Simple Interest = PRT / 100
=$4500 × 1.7 × 5 / 100
=$38250 / 100
=$382.50
Simple interest =$382.50
Total amount = $4500 + $382.50
=$4882.50
Therefore, the total amount in the account after five years is $4882.50
In a hospital ward, there are 15 nurses and 3 doctors. 9 of the nurses and 1 of the doctors are female. If a person is randomly selected from this group, what is the probability that the person is male or a doctor?
Answer:
i believe the answer is 9/18
5. In what quadrant is the angle 237° located?
A. IV
B. II
C. I
D. III
Final answer:
The angle 237° is located in the third quadrant since it is between 180° and 270°.Therefore, the correct answer to the question is:
D. III
Explanation:
The question asks in which quadrant the angle 237° is located. To determine the quadrant of an angle in standard position (angle measured from the positive x-axis), we use the following information:
Angles from 0° to 90° are in the first quadrant.
Angles from 90° to 180° are in the second quadrant.
Angles from 180° to 270° are in the third quadrant.
Angles from 270° to 360° are in the fourth quadrant.
Since 237° is between 180° and 270°, it is located in the third quadrant. Therefore, the correct answer to the question is:
D. III
The wheels on Jason's dirt bike measure 19 inches in diameter. How many revolutions will the wheels make when Jason rides for 500 feet? Use 3.14 for ?. Round to the nearest whole revolution.
Answer: 101 revolutions
Step-by-step explanation:
Answer: The total number of revolutions is 101.
Step-by-step explanation: Given that the wheels on Jason's dirt bike measure 19 inches in diameter.
We are to find the number of revolutions that the wheels make when Jason rides for 500 feet.
We know
1 foot = 12 inches.
So, 500 feet = 12 × 500 = 6000 inches.
Now, diameter of the wheels is given by
d = 19 inches.
So, the circumference of the wheels will be
[tex]C=\pi d=3.14\times19=59.66~\textup{inches}.[/tex]
Therefore, to ride 500 feet, The number of revolutions that the wheels make is given by
[tex]n=\dfrac{6000}{59.66}=100.56989...[/tex]
Rounding to the nearest whole number, the required number of revolutions will be 101.
Thus, the total number of revolutions is 101.
The equation of the graphed line in point-slope form is?, and it’s equation in slope-intercept form is?
ANSWER
Point-slope form:
[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]
Slope-intercept form:
[tex]y= -\frac{3}{5} x + \frac{9}{5}[/tex]
EXPLANATION
The graphed line passes through
[tex](-2,3) \: \: and \: \: (3,0)[/tex]
The slope of this line is determined using
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
We substitute the points to get;
[tex]m = \frac{0 - 3}{3 - - 2} [/tex]
[tex]m = -\frac{3}{5} [/tex]
The point-slope formula is:
[tex]y-y_1 = m(x - x_1)[/tex]
Substitute the first point and slope to get:
[tex]y - 3 = -\frac{3}{5} (x - - 2)[/tex]
[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]
To find the slope-intercept form, we expand to get:
[tex]y= -\frac{3}{5} x - \frac{6}{5} + 3[/tex]
[tex]y= -\frac{3}{5} x + \frac{9}{5} [/tex]
Answer:
Slope
[tex]m=-\frac{3}{5}[/tex]
point-slope form
[tex]y=-\frac{3}{5}(x-3)[/tex]
slope-intersection form
[tex]y=-\frac{3}{5}x+1.8[/tex]
Step-by-step explanation:
The equation of a line in the point-slope form has the following formula:
[tex]y-y_0 = m (x-x_0)[/tex]
Where m is the slope and [tex](x_0, y_0)[/tex] is a point belonging to the line.
The equation of a line in the slope-intersection form has the following formula:
[tex]y = mx + b[/tex]
Where b is the intersection of the line with the y axis.
To calculate the slope of the line knowing 2 points we use the following formula:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]
In this case:
[tex]x_0 =3\\y_0=0\\x_1=-2\\y_1=3[/tex]
So
[tex]m=\frac{3-0}{-2-3}[/tex]
[tex]m=-\frac{3}{5}[/tex]
So the equation of a line in the point-slope form
[tex]y-0 =-\frac{3}{5}(x-3)[/tex]
[tex]y=-\frac{3}{5}(x-3)[/tex]
The equation of a line in the slope-intersection form is:
[tex]y-0=-\frac{3}{5}(x-3)[/tex]
[tex]y=-\frac{3}{5}(x-3)[/tex]
[tex]y=-\frac{3}{5}x+\frac{9}{5}[/tex]
[tex]y=-\frac{3}{5}x+1.8[/tex]
with [tex]b=1.8[/tex]
Scores on a history test have average of 80 with standard deviation of 6. What is the z-score for a student who earned a 75 on the test? Round your answer to the nearest thousandth.
The z-score for a student who scored 75 on the test with an average of 80 and a standard deviation of 6 is approximately -0.833, indicating the score is 0.833 standard deviations below the mean.
To calculate the z-score for a student who scored 75 on a history test, we can use the z-score formula:
[tex]Z = \( \frac{X - \mu}{\sigma} \)[/tex]
Where:
X is the raw score (75 in this case)
[tex]\( \mu \)[/tex] is the mean score (80)
[tex]\( \sigma \)[/tex] is the standard deviation (6)
Inserting the values, we get:
[tex]Z = \( \frac{75 - 80}{6} \) = \( \frac{-5}{6} \) = -0.833\[/tex]
The z-score for a student who earned 75 on the test is approximately -0.833, rounded to the nearest thousandth. This z-score indicates that the student's score is about 0.833 standard deviations below the mean
Find the sum of the infinite geometric series, if it exists.
4 - 1 + 1/4 - 1/16 + . . .
a. -1
b. 16/5
c. 3
d. does not exist
So the series looks something like this:
[tex]\Sigma_{n=4}^{\infty}\frac{n-1}{16} \\
\frac{1}{16}\Sigma_{n=4}^{\infty}n-1[/tex]
If [tex]\lim_{n\rightarrow\infty}\neq[/tex] than [tex]\Sigma{a_n}[/tex] diverges. So we must apply limit infinity property:
[tex]\lim_{n\rightarrow\infty}(ax^n+\dots+bx+c)=\infty, a>0[/tex] and n is odd.
So...
[tex]\lim_{n\rightarrow\infty}n-1=\infty[/tex]
The series diverges.
Hope this helps.
r3t40
Please help, refer to the picture for information.
Answer:
b
Step-by-step explanation:
Using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)
d = [tex]\sqrt{(4+1)^2+(1-4)^2}[/tex]
= [tex]\sqrt{5^2+(-3)^2}[/tex]
= [tex]\sqrt{25+9}[/tex] = [tex]\sqrt{34}[/tex] → b
Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of the summer. He withdraws $28 each week for food. Which inequality represents w, the number of weeks Manuel can withdraw money while not dropping below a $300 balance?
28-600w < 300
28-600w > 300
600-28w < 300
600-28w > 300
Answer: C (600 - 28w < 300)
I know this because: I took the E2020 test
Answer:
Answer: C (600 - 28w < 300)
Step-by-step explanation:
What is the equation of the parabola with focus (1,1/2) and directrix y=3
Answers:
A. Y=-1/5x^2+2/5x+31/20
B. Y=-3/16x^2
C. Y=-3/5x^2-14/31x+71/16
D. Y=-x^2+17x-1
A jumbo crayon is composed of a cylinder with a conical tip. The cylinder is 12 cm tall with a radius of 1.5 cm, and the cone has a slant height of 2 cm and a radius of 1 cm. The lateral area of the cone is π cm2. To wrap paper around the entire lateral surface of the cylinder, π cm2 of paper is needed. The surface area, including the bottom base of the crayon, is π cm2.
Answer:
Part 1) The lateral area of the cone is [tex]LA=2\pi\ cm^{2}[/tex]
Part 2) The lateral surface area of the cylinder is [tex]LA=36\pi\ cm^{2}[/tex]
Part 3) The surface area of the crayon is [tex]SA=41.50\pi\ cm^{2}[/tex]
Step-by-step explanation:
Part 1) Find the lateral area of the cone
The lateral area of the cone is equal to
[tex]LA=\pi rl[/tex]
we have
[tex]r=1\ cm[/tex]
[tex]l=2\ cm[/tex]
substitute
[tex]LA=\pi (1)(2)[/tex]
[tex]LA=2\pi\ cm^{2}[/tex]
Part 2) Find the lateral surface area of the cylinder
The lateral area of the cylinder is equal to
[tex]LA=2\pi rh[/tex]
we have
[tex]r=1.5\ cm[/tex]
[tex]h=12\ cm[/tex]
substitute
[tex]LA=2\pi (1.5)(12)[/tex]
[tex]LA=36\pi\ cm^{2}[/tex]
Part 3) Find the surface area of the crayon
The surface area of the crayon is equal to the lateral area of the cone, plus the lateral area of the cylinder, plus the top area of the cylinder plus the bottom base of the crayon
Find the area of the bottom base of the crayon
[tex]A=\pi[r2^{2}-r1^{2}][/tex]
where
r2 is the radius of the cylinder
r1 is the radius of the cone
substitute
[tex]A=\pi[1.5^{2}-1^{2}][/tex]
[tex]A=1.25\pi\ cm^{2}[/tex]
Find the area of the top base of the cylinder
[tex]A=\pi(1.5)^{2}=2.25\pi\ cm^{2}[/tex]
Find the surface area
[tex]SA=2\pi+36\pi+2.25\pi+1.25\pi=41.50\pi\ cm^{2}[/tex]
Answer:
2
36
41.5
Step-by-step explanation:
just got it all right even though I guessed soooo, yay
Step-by-step explanation:
Can someone please show me how
19169000*e^(0.15)= 222712201
When e= 2.7182818284?
Answer:
It doesn't. x = 22 271 201
Step-by-step explanation:
You are going to need a calculator no matter how you do it.
[tex]x =19 169 000 \times e^{0.15}[/tex]
(a) The direct method
[tex]x = 19 169 000\times 2.718 281 828^{0.15} = 19 169 000 \times 1.161 834 243 = 22 271 201[/tex]
(b) The indirect method
[tex]\ln \left (19 169 000\times 2.718 281 828^{0.15} \right ) = \ln(19 169 000) + 0.15 = 16.768 805 + 0.15 = 16.918 804\\\\e^{16.918 804} = 22 271 201[/tex]
Which of the following graphs is described by the function given below?
y = 2x^2 + 8x +3
Answer:
A
Step-by-step explanation:
y = 2x² + 8x + 3
Complete the square:
y = 2(x² + 4x) + 3
y = 2(x² + 4x + 4) + 3 - 2(4)
y = 2(x + 2)² - 5
So the vertex is at (-2, -5). The graph must be Graph A.
Graph A has its vertex at (-4, -5). Then the correct option is A.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The parabolic expression is given below.
y = 2x² + 8x + 3
y = 2(x² + 4x) + 3
y = 2(x² + 4x + 4) - 8 + 3
y = 2(x + 4)² -5
The vertex of the parabola is at (-4, -5).
Graph A has its vertex at (-4, -5). Then the correct option is A.
Then the graph of the parabola is given below.
More about the parabola link is given below.
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What is the missing coefficient of the x-term of the product (-x-5)2 after it has been simplified?
Answer:
The missing coefficient of the x-term of the product (-x-5)2 is 10.
Step-by-step explanation:
Solution:Through whole square formula.
(-x-5)2 = (-x)^2 -2(-x)(5)+(5)^2
=x^2+10x+25
Therefore, the missing coefficient of the x-term of the product is 10
Answer:
10
Step-by-step explanation:
The given expression is
[tex](-x-5)^2[/tex]
We need to find the coefficient of x.
According to the property of algebra.
[tex](a-b)^2=a^2-2ab+b^2[/tex]
In the given expression a=-x and b=5.
Substitute a=-x and b=5 in the above formula.
[tex](-x-5)^2=(-x)^2-2(-x)(5)+(5)^2[/tex]
On further simplification we get
[tex](-x-5)^2=x^2+10x+25[/tex]
Coefficient of x is a multiplicative factor of x.
Therefore, the coefficient of x is 10.
[tex]\frac{a}{x-8} +\frac{b}{x+4} =\frac{2x-64}{(x-8)(x+4)}[/tex]
solve for a and b
Answer:
a = -4
b = 6
Step-by-step explanation:
See attached
Answer:
a=-4 and b=6
Step-by-step explanation:
[tex]\frac{a}{x-8} +\frac{b}{x+4} =\frac{2x-64}{(x-8)(x+4)}[/tex]
First, add the fractions by finding the common denominator.
In this case, (x-8)(x+4).
[tex]\frac{a(x+4) + b(x-8)}{(x-8)(x+4)} =\frac{2x-64}{(x-8)(x+4)}[/tex]
Therefore, the numerators are equal:
[tex]a(x+4) + b(x-8) =2x-64[/tex]
Simplify:
[tex]ax+4a + bx-8b =2x-64\\(a+b)x+4a-8b=2x-64[/tex]
Now match the coefficients.
[tex]a+b=2, 4a-8b=-64[/tex]
Solve the system of equations. I'll use substitution, but you can also use elimination if you prefer.
[tex]4a-8b=-64\\a-2b=-16\\(2-b)-2b=-16\\2-3b=-16\\-3b=-18\\b=6\\a=-4[/tex]
Therefore, a=-4 and b=6.
The recyclables have been sorted into plastic and glass. The number of plastic items is 30 less than nine times the number of glass items. The recyclables are 85% plastic. How many glass items are there?
a. 6
b. 9
c. 15
d. 18
Answer:
B
Step-by-step explanation:
We will use substitution method after writing 2 equations to solve for number of glass items.
Let number of glass items be g and number of plastic items be p
"The number of plastic items is 30 less than nine times the number of glass items":
We can write the equation as [tex]p=9g-30[/tex]
"The recyclables are 85% plastic":
This means that plastic (p) is 0.85 of the total (p+g). Thus we can write equation as [tex]p=0.85(p+g)[/tex]
We can substitute the expression for p in first equation into 2nd and solve for g:
[tex]p=0.85(p+g)\\(9g-30)=0.85((9g-30)+g)\\9g-30=0.85(10g-30)\\9g-30=8.5g-25.5\\0.5g=-25.5+30\\0.5g=4.5\\g=\frac{4.5}{0.5}\\g=9[/tex]
The number of glass items is 9
Answer:
b. 9
Step-by-step explanation:
x : glass items
9x - 30 : plastic items
(the equation will be set equal to [tex]\frac{15}{85}[/tex] because 85% of the recyclables are plastic, so that means 15% must be glass.)
[tex]\frac{x}{9x-30} =\frac{15}{85}[/tex]
[tex]85x=135x-450[/tex] (now subtract 135x from each side to isolate x to one side of the equation)
[tex]-50x=-450[/tex] (divide each side of the equation by -50 to isolate x)
[tex]x=9[/tex]
Please dont ignore, need help) Write the ratios for sin P and cos Q
Answer: both are 21/29
Step-by-step explanation:
Use SOHCAHTOA so the opposite/hypotenuse for P is 21/29 and the adjacent/hypotenuse for Q is also 21/29
How many possible rational roots are there for 2x4+4x3−6x2+15x−12=0?
A. 4
B. 6
C. 8
D. 12
E. 16
Final answer:
Using the Rational Root Theorem, the polynomial equation 2x⁴+ 4x³-6x²+15x-12=0 has 12 distinct possible rational roots, where factors of the constant term are divided by factors of the leading coefficient.
Explanation:
To determine the number of possible rational roots for the polynomial equation 2x⁴+4x³−6x²+15x−12=0, we can use the Rational Root Theorem. This theorem states that if the polynomial has any rational roots, they must be of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The constant term in this case is -12, and its factors are ±1, ±2, ±3, ±4, ±6, and ±12. The leading coefficient is 2, and its factors are ±1 and ±2.
Thus, the possible rational roots are combinations of the factors of -12 divided by the factors of 2, giving us ±1, ±2, ±3, ±4, ±6, and ±12 combined with ±1 and ±2. So, our possible rational roots are: ±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±12/1, ±1/2, ±2/2, ±3/2, ±4/2, ±6/2, and ±12/2 which simplifies to ±1/1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, and ±6/2.
After simplification, there is a total of 12 distinct possible rational roots, corresponding to option D.